Problem: Simplify the following expression: $q = \dfrac{-35y - 20}{15y - 40}$ You can assume $y \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-35y - 20 = - (5\cdot7 \cdot y) - (2\cdot2\cdot5)$ The denominator can be factored: $15y - 40 = (3\cdot5 \cdot y) - (2\cdot2\cdot2\cdot5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $q = \dfrac{(5)(-7y - 4)}{(5)(3y - 8)}$ Dividing both the numerator and denominator by $5$ gives: $q = \dfrac{-7y - 4}{3y - 8}$